To find \((g \circ f)(-1)\), we first need to compute \(f(-1)\) and then use that result to find \(g(f(-1))\).
- Calculate \(f(-1)\):
\[ f(x) = -x + 3 \]
Substituting \(-1\) for \(x\):
\[ f(-1) = -(-1) + 3 = 1 + 3 = 4 \]
- Next, we need to calculate \(g(f(-1)) = g(4)\):
\[ g(x) = 2x + 1 \]
Substituting \(4\) for \(x\):
\[ g(4) = 2(4) + 1 = 8 + 1 = 9 \]
So, \((g \circ f)(-1) = g(f(-1)) = g(4) = 9\).
Thus, the answer is:
\[ (g \circ f)(-1) = 9 \]